A refined Razumov-Stroganov conjecture II

TL;DR

This paper extends a conjecture linking the Perron-Frobenius eigenvector of a monodromy matrix in the O(1) loop model to refined counts of alternating sign matrices, exploring new configurations with dislocations.

Contribution

It introduces a refined conjecture connecting the eigenvector to specific ASM counts on a semi-infinite cylinder with dislocations, revealing deeper model correspondences.

Findings

Generated the ASM counting function with prescribed 1's positions.

Established a connection between the monodromy matrix eigenvector and ASM refinements.

Indicated a deep correspondence between observables in the O(1) loop model and ASM counts.

Abstract

We extend a previous conjecture [cond-mat/0407477] relating the Perron-Frobenius eigenvector of the monodromy matrix of the O(1) loop model to refined numbers of alternating sign matrices. By considering the O(1) loop model on a semi-infinite cylinder with dislocations, we obtain the generating function for alternating sign matrices with prescribed positions of 1's on their top and bottom rows. This seems to indicate a deep correspondence between observables in both models.